The present invention relates to a method for determining at least one optimal trajectory for reaching a fuzzy target in a three-dimensional medium starting from a point remote from the target.
In oil exploration, it is standard practice to seek to reach by drilling a geological structure situated in the subsurface and which might contain hydrocarbons. Very often, the start point for the drilling is positioned so as to take various constraints into account, in particular on-shore environmental constraints or off-shore optimization constraints.
Along with the growth in off-shore drilling, on account of the very high costs of marine production structures, it has been necessary to develop sophisticated techniques of directional drilling such that a single drilling start point can give access to several geological structures lying greater or lesser distances away in the subsurface. As a consequence of this, it is necessary to optimize the positioning of the production platform so as to obtain best access to all the sought-after geological structures. Therefore, the boreholes emanating from marine platforms sprout like upturned blooms in the subsurface. Ideally, the trajectory of a borehole lies in a vertical plane of chosen azimuth. It consists of a succession of rectilinear segments and arcs of circles strung together. The deviation of the borehole may be such that the trajectory of the borehole switches from a vertical direction at the origin to a horizontal direction when penetrating the geological structure.
A first problem has been knowing where the drilling tool was located at each instant during the progress of the borehole. This difficulty has been overcome firstly off-line through the use of single-shot, and then multi-shot photographic techniques which have made it possible to ascertain the azimuth and the inclination of the trajectory at regular intervals. These two measurements, allied with the drilled length, deduced from the length of the drill pipes, have made it possible to calculate the actual trajectory and hence the coordinates x, y, z of each measurement point in a three-dimensional orthonormal reference frame with the drilling kick-off as origin.
A second problem was knowing how to direct the drilling, in real time, towards a target point of the subsurface in as accurate a manner as possible. This technique did not experience a real upsurge until the development of directional turbodrilling associating the use of a downhole motor and a bent coupling. Initially, the measurements were carried out off-line by the single-shot photographic technique with each addition of drill pipes. Thereafter, the development of a special tool fitted with magnetometers and accelerometers and incorporated into the drill string (MWD standing for xe2x80x9cMeasurement While Drillingxe2x80x9d) has made it possible to transmit azimuth and inclination of the trajectory in real time without interrupting drilling operations. More recently, the designing of flexible drill pipes has made it possible to reduce considerably the radii of curvature of trajectories, thus making it possible to switch from the vertical to the horizontal within a few tens of meters.
The duration of drilling is a critical parameter on account of the costs which it entails. This duration should therefore be reduced to a minimum. An effective way of reducing the duration of drilling is to reduce the trajectory of the drilling to an optimal length, for example a minimum. The problem of calculating the trajectory of the borehole from the start point to the location of the structure in the subsurface has thus been proposed. Posed in these terms, the problem has been solved for a number of years now. Thus, the Wellbore Planner(copyright) software, marketed by Landmark, makes it possible, among other things, to calculate various well trajectories deviated towards target structures chosen in the subsurface. Likewise, the article by M. Wael Helmi, F. Khalef, T. Darwish, entitled xe2x80x9cWell design using computer modelxe2x80x9d and published by the Society of Petroleum Engineers SPE 37709 of 15-18/03/97, pages 299-307, proposes a method for calculating the trajectory of a borehole of minimum length between a start point and a target situated in the subsurface.
However, there is still a major obstacle to the complete effectiveness of the trajectory calculation, namely the uncertainty regarding the knowledge of the subsurface. Indeed, the subsurface is generally explored with the aid of seismic campaigns whose results are nowadays 3D seismic blocks. Depth migrations, which provide depthwise images of the subsurface, can be carried out using these seismic blocks. Chiefly distinguishable in these images are wave reflectors, called seismic horizons, which often correspond to boundaries of geological structures, which structures are the major objectives of oil exploration.
Whereas the shape of the geological structure may be relatively clearly apparent, its position in the subsurface is not accurately guaranteed since the depth migrations rely on approximate models of wave propagation velocities in the subsurface. It is therefore appreciated that the result of an uncertainty with regard to the velocity models causes, on concluding the calculations required for the migration, an uncertainty as to the position of the structures in the subsurface. In particular, this uncertainty becomes crucial when, for example, the structure is crossed by a fault dividing it into a compartment regarded as a hydrocarbon trap and a compartment containing no hydrocarbons, and when one wishes specifically to reach the hydrocarbon trap compartment and definitely not the other. Under these conditions, an error of a few meters in the position of the structure then becomes a source of major difficulties which translate into so many additional expenses to remedy same.
The consequences of imprecise knowledge regarding the position of structures were pointed out long ago and various studies have attempted to take them into account. In particular, in an article published in the JPT journal of February 1994, pages 143-149, published by the Society of Petroleum Engineers and entitled xe2x80x9cA multidisciplined approach to designing targets for horizontal wellsxe2x80x9d, the authors S. T. Solomon et al focused on defining a target structure in three dimensions together with a certain tolerance. Their approach is based on a multidisciplinary consensus. The various petroleum professionals having defined their own view of the target are led to quantify reasonable uncertainties with regard to their specific parameters. For example, geologists and geophysicists advise of the uncertainty due to depth migration and reservoir specialists the uncertainties regarding the planes of contact of the fluids contained in the trap. These various uncertainties are subsequently weighted one against another. The final result is then a global volume, referred to as a target diagram, defined by the sum of the various volumes associated with each of the uncertain parameters. Specifically, with any contact point X known with uncertainty dX, there is associated the volume V(X) lying between Xxe2x88x92dX and X+dX. The objective of the drilling, horizontal in this instance, is then as far as possible to reach the centre of the global volume.
As interesting as it may be, this approach does not offer the driller a trajectory. The driller will be allocated a target volume to be reached and it falls to him to choose the best trajectory to get there.
The subject of the present invention is a method of determining an optimal trajectory for reaching a target situated in a medium, for example the subsurface, and whose position is known in an uncertain manner, the said method making it possible to remedy the drawbacks and inadequacies of the prior techniques.
The method according to the invention for determining at least one optimal trajectory starting from a predetermined point of a medium so as to reach a target situated in this medium and comprising a centre and a peripheral boundary, the said target forming a centred volume, the position of each of whose points is known with geometrical uncertainties, is characterized in that it consists in:
defining for the centred volume a gain which takes a first value at the centre of the said centred volume, a second value lower than the said first value at each of the points of the peripheral boundary, intermediate values at each of the other points of the said centred volume and a zero value outside the centred volume,
determining a statistically significant number of instances of the positions of the centred volume as a function of the geometrical uncertainties which affect it,
summing at each point of the medium the values taken by the gain for the various positions of the centred volume so as to obtain an aggregate gain at each point,
defining a volume of interest, site of the points with positive aggregate gains in the medium,
defining curvilinear trajectories which pass through the volume of interest from at least one entry point of the volume of interest to at least one exit point of the said volume of interest,
integrating the aggregate gain along each of the said curvilinear trajectories in such a way as to obtain a profit associated with each trajectory, and
retaining all the trajectories whose profit is greater than a threshold.
According to another characteristic of the invention, the statistically significant number of instances is obtained by random drawing.
According to another characteristic of the invention, geometrical uncertainty vectors are allocated to each point of the medium and the resultant uncertainty vector is calculated, which is assigned to the said point of the medium.
According to another characteristic of the invention, the medium is a portion of subsurface enclosing seismic horizons defined by a depth migration of seismic data relating to the said portion, and three geometrical uncertainty vectors are allocated to each point of the medium, these being an uncertainty vector regarding the picking of the horizons, an uncertainty vector regarding the depth migration and an uncertainty vector regarding seismic tie of the horizons with respect to at least one borehole of the medium so as to calculate the resultant vector.
According to another characteristic of the invention, at each point of the medium, the geometrical uncertainty vectors vary in magnitude without varying in direction.
According to another characteristic of the invention, the directions of the uncertainty vectors are predetermined.
According to another characteristic of the invention, at neighbouring points of the centred volume, the magnitudes of the resultant uncertainty vectors exhibit values such that the said neighbouring points are not displaced independently during the displacement of the centred volume.
According to another characteristic of the invention, when fractures pass through the centred volume, the gain associated with all the points of the centred volume which are separated from the centre of the target by at least one fracture is zeroed.
According to another characteristic of the invention, when the centred volume contains seismic horizons through which there passes at least one fault, the points of contact of the horizons with the fault are securely attached during the displacement of the centred volume.
According to another characteristic of the invention, among the trajectories whose profit is above a threshold, those trajectories are selected which optimize a predetermined criterion such as that which minimizes the cost of drilling or the length of the trajectory.
According to another characteristic of the invention, the medium enclosing the target is bounded by an upper surface and the trajectory possesses a start point situated in the medium, between the target and the said surface or on this surface.
Advantageously, for the implementation of the method according to the invention, the medium enclosing the centred volume is represented in the form of a three-dimensional meshed network with axes x, y and z which comprises nodes whose position is known with a geometrical uncertainty I, which is defined by a vector having components Ix, Iy and Iz along the three axes of the medium and represented by three statistical density functions. In particular, when the said medium is a portion of subsurface which encloses seismic horizons and faults, defined by a depth migration of seismic data relating to the said portion, a meshing of the medium is carried out which includes a meshing of the horizons and the faults detected after the depth migration of the seismic block. Indeed, the layer boundaries (horizons) and fault boundaries are favoured supports of the mesh. More precisely, the meshing of the subsurface is carried out with the aid of structural maps deduced from seismic surveying, which maps are in general tied to exploration wells.
For an implementation of the method according to the invention by using the said meshed network:
the target is defined as a target node C of the medium surrounded by a neighbourhood V, which is a meshed volume contained in the medium and affected at each of its nodes by the geometrical uncertainties of the medium, which are represented by uncertainty vectors whose resultant is formed at each node,
a fixed node D contained in the medium and situated outside the neighbourhood V is chosen as start point of the trajectory,
a maximum gain is assigned to the target node C and a decreasing gain is assigned to the nodes included in the neighbourhood V as a function of distance away from the target node C, down to a minimum gain at the periphery of the neighbourhood V, and a zero gain is assigned to all the nodes of the medium outside the neighbourhood V,
random drawing is carried out for the magnitudes of the uncertainty vectors at each node of the target and each node is displaced along the resultant uncertainty vector allocated to it, each set of new locations of the nodes constituting an instance of position of the target,
the gains deduced from each instance of position of the target (C, V) are summed at each node of the medium and the aggregate gain is allocated to the node concerned,
a volume of interest is defined, site of the nodes of the medium whose aggregate gain is positive,
the volume of interest is inscribed within a parallelepiped oriented along the three axes of the medium,
an entry face and an exit face are chosen on the parallelepiped,
the entry and exit faces of the parallelepiped are meshed,
a profit is calculated for all the rectilinear segments of each trajectory connecting each of the nodes of the mesh of the entry face to all the nodes of the mesh of the exit face, the said profit being the sum of the aggregate gains allocated to the nodes of those mesh cells of the volume of interest through which the segment passes,
the set of segments of the trajectories exhibiting a profit above a first threshold is preserved,
the segments of the preserved trajectories are joined to the start node D so as to obtain final trajectories and a cost is calculated for each of the said trajectories, and
the final trajectories having a cost below a second threshold are selected as optimal final trajectories connecting the start node D to the target node C.
In the implementation of the method explained hereinabove, the medium is a meshed portion of subsurface containing faults and a zero gain is assigned to all the nodes of the neighbourhood V which are separated from the target node C by at least one fault.